Active resonator system with tunable quality factor, frequency, and impedance

ABSTRACT

Active feedback is used with two electrodes of a four-electrode capacitive-gap transduced wine-glass disk resonator to enable boosting of an intrinsic resonator Q and to allow independent control of insertion loss across the two other electrodes. Two such Q-boosted resonators configured as parallel micromechanical filters may achieve a tiny 0.001% bandwidth passband centered around 61 MHz with only 2.7 dB of insertion loss, boosting the intrinsic resonator Q from 57,000, to an active Q of 670,000. The split capacitive coupling electrode design removes amplifier feedback from the signal path, allowing independent control of input-output coupling, Q, and frequency. Controllable resonator Q allows creation of narrow channel-select filters with insertion losses lower than otherwise achievable, and allows maximizing the dynamic range of a communication front-end without the need for a variable gain low noise amplifier.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.15/351,047 filed on Nov. 14, 2016, incorporated herein by reference inits entirety, which is a 35 U.S.C. § 111(a) continuation of PCTinternational application number PCT/US2015/031251 filed on May 15,2015, incorporated herein by reference in its entirety, which claimspriority to, and the benefit of, U.S. provisional patent applicationSer. No. 61,993,554 filed on May 15, 2014, incorporated herein byreference in its entirety. Priority is claimed to each of the foregoingapplications.

The above-referenced PCT international application was published as PCTInternational Publication No. WO 2015/176041 on Nov. 19, 2015, whichpublication is incorporated herein by reference in its entirety.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with Government support under FA9550-10-1-0293awarded by the Department of Defense, Defense Advanced Research ProjectsAgency (DARPA). The Government has certain rights in the invention.

NOTICE OF MATERIAL SUBJECT TO COPYRIGHT PROTECTION

A portion of the material in this patent document is subject tocopyright protection under the copyright laws of the United States andof other countries. The owner of the copyright rights has no objectionto the facsimile reproduction by anyone of the patent document or thepatent disclosure, as it appears in the United States Patent andTrademark Office publicly available file or records, but otherwisereserves all copyright rights whatsoever. The copyright owner does nothereby waive any of its rights to have this patent document maintainedin secrecy, including without limitation its rights pursuant to 37C.F.R. § 1.14.

BACKGROUND

1. Technical Field

The technology of this disclosure pertains generally to filters, andmore particularly to filters using microelectromechanical systems(MEMS).

2. Background Discussion

Power consumption in electronics is a continual area of research. Lowerpower produces longer device life, and hopefully leads to sensor motesthat will never require battery replacement during their usefullifetimes.

BRIEF SUMMARY

A basic Q-boosted filter uses active feedback to boost an intrinsic Q ofa MEMS resonator. Combing multiple such resonators, either mechanicallyor electrically, allows construction of filters with narrower passbandand improved loss compared with unboosted resonator elements. In oneembodiment, the base resonator uses a four electrode resonator to enableboosting of the intrinsic disk resonator Q, and to allow independentcontrol of insertion loss across the two other electrodes.

In one example, two such Q-boosted resonators are configured as parallelmicromechanical filters to achieve a tiny 0.001% bandwidth passbandcentered around 61 MHz with only 2.7 dB of insertion loss, by boostingthe intrinsic disk resonator Q from 57,000, to an active Q of 670,000.

The split capacitive coupling electrode design removes amplifierfeedback from the signal path, allowing for the independent control ofinput-output coupling, Q, and frequency. Controllable resonator Q allowscreation of narrow channel-select filters with insertion losses lowerthan otherwise achievable, and allows maximizing the dynamic range of acommunication front-end without the need for a variable gain low noiseamplifier.

Active feedback is used with two electrodes of a four-electrodecapacitive-gap transduced wine-glass disk resonator to enable boostingof an intrinsic resonator Q and to allow independent control ofinsertion loss across the two other electrodes. This Q-boosting filterapproach applies to many other resonator varieties beyond this examplecapacitive-gap device, however.

Controllable resonator Q allows for the creation of narrowchannel-select filters with insertion losses lower than otherwiseachievable, and allows maximizing the dynamic range of a communicationfront-end without the need for a variable gain low noise amplifier. Byforegoing the LNA, power consumption is reduced, allowing for filtersthat operate in the sub-mW range.

By using two such Q-boosted filters in parallel, a nearly flat, butextremely narrow, pass band may be produced. Signals outside the passband are quickly attenuated.

Further aspects of the technology described herein will be brought outin the following portions of the specification, wherein the detaileddescription is for the purpose of fully disclosing preferred embodimentsof the technology without placing limitations thereon.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)

The technology described herein will be more fully understood byreference to the following drawings which are for illustrative purposesonly:

FIG. 1 is a schematic of a Q-boosted parallel filter comprised of twoindependent wine-glass disk resonator and amplifier circuits, all in atypical measurement circuit.

FIG. 2A is a detailed schematic of an active Q-controlled resonator,where a transimpedance amplifier provides closed-loop feedback using twoelectrodes of a wine-glass resonator, while the remaining two electrodesserve as input and output.

FIG. 2B is a schematic of the major components of the activeQ-controlled resonator.

FIG. 2C is a modal analysis output depicting a mode shape of thewine-glass resonator.

FIG. 3 is a schematic of an equivalent small signal circuit model forthe Q and insertion loss adjustable of the active Q-controlled resonatorof FIG. 2A through FIG. 2C, with ports 1-2 used for input and output andports 3-4 embedded in a feedback loop with a transimpedance amplifier toenable control of Q.

FIG. 4 is a graph of theoretically predicted resistance (dashed line)and reactance (solid line) parts of the impedance, Z_(amp), looking intothe TIA amplifier as the feedback resistor, R_(F), increases, usingapproximate resistance and capacitance values for the amplifier for thesimulation.

FIG. 5A is a detailed transimpedance amplifier circuit comprising afully differential CMOS amplifier with one end connected in shunt-shuntfeedback, and output taken from the other end to realize a 0°input-output phase shift. Transistor M_RF serves as a voltagecontrollable shunt-shunt feed-back resistor, allowing easy adjustment ofTIA gain via its gate voltage V_(GAIN).

FIG. 5B is a photomicrograph of the fabricated amplifier applicationspecific integrated circuit (ASIC).

FIG. 5C is a graph of gain versus frequency of the device of FIG. 5A.

FIG. 5D is a graph of phase versus frequency of the device of FIG. 5A.

FIG. 6A is a graph of transmission versus frequency of parallel filteroperation, where two differentially driven bandpass biquad responses addto form a flat passband (between the peaks) and subtract in the stopband(outside the peaks) to provide greater stopband rejection.

FIG. 6B is a graph of phase versus frequency of the parallel filteroperation previously modeled in FIG. 6A.

FIG. 7A is a graph of simulated parallel filter responses for a narrow0.002% bandwidth filter with low Q (the intrinsic device Q) equivalentto 1.36×BW_(fil), Q-boosted by 2×, and 22×, for constant R_(Q), with aninsertion loss improvement of about 12 dB.

FIG. 7B is a graph of the simulated parallel filter response of FIG. 7Athat illustrates that the filter can be terminated properly by adjustingthe bias voltage across input and output gaps while R_(Q) is keptconstant.

FIG. 8A is a cross section illustrating one embodiment of a MEMSresonator prior to resonator disk release in 49% HF.

FIG. 8B is a cross section of the MEMS resonator of FIG. 8A afterresonator disk release in 49% HF.

FIG. 8C is a scanning electron micrograph (SEM) of the device of FIG.6B, which was used in this disclosure.

FIG. 9A is a graph of transmission versus frequency for single resonatorQ-boosting as a function of amplifier gain with constant V_(P)=8.5 V.

FIG. 9B is a graph of the transmission versus frequency of a singleresonator Q-boosting device demonstrating independent tuning offrequency and insertion loss via control of the voltage acrossinput-output electrode-disk gap, all while holding Q constant by holdingV_(GAIN) constant.

FIG. 10 is a graph of measured effective quality factor and insertionloss of the resonator with constant V_(P)=8.5 V as V_(GAIN) of theamplifier changes.

FIG. 11A is a graph of measured transmission versus frequency for atwo-resonator active Q-controlled resonator arranged in a circuit asshown in FIG. 1.

FIG. 11B is a graph of the group delay in ms versus frequency of thedevice previously shown in FIG. 11A.

FIG. 12 is a schematic of one embodiment of a Q-boosted parallel filtercomprised of two independent wine-glass disk resonators and a singleamplifier circuit used to boost Q of both resonators.

DETAILED DESCRIPTION

I. Introduction

The increasing role of wireless technology in our daily lives isaccompanied by a need for reduced radio power consumption. This will beespecially important as wireless devices become ubiquitous, going beyondthe smart phones of today to perhaps networks of more than a trillionautonomous sensors of tomorrow—sensors for which no one wants to replacebatteries. Among components in a typical radio receiver, the front-endfilters play a pivotal role in reducing power consumption. Inparticular, by removing unwanted blockers before they reach front-endelectronics, these filters allow such electronics to operate with lowerdynamic range than would otherwise be needed, hence, with lower powerconsumption.

From this perspective, the high-Q surface acoustic wave (SAW) and thinfilm acoustic resonator (FBAR) vibrating mechanical devices that make uptoday's radio frequency (RF) bandpass filters are already responsiblefor significant power savings in wireless handsets. Indeed, their Qs inthe low thousands make possible 3% bandwidth filters that rejectpotentially large out-of-band interferers immediately after the antenna,allowing for significant low noise amplifier (LNA) and mixer dynamicrange reductions.

Still, there is room for improvement. In particular, although goodenough to select a frequency band of many channels, the Qs attainable bycommercial resonator technology are not sufficient to realize filterswith bandwidths small enough to select single channels. If possible,such a capability would allow removal of not only out-of-bandinterferers, but also in-band ones. This would then provide severalorders more reduction in power consumption, not just from reduceddynamic range, but also due to the availability of much more efficientreceiver architectures when there are no interferers.

Unfortunately, the resonator Q required for such a channel-selectingfilter is quite daunting. For example, a 400-kHz bandwidth filterdesigned to select a single 200-kHz wide GSM-850 channel (and reject allothers) would need constituent resonators with Qs greater than 15,000 tomaintain less than 2 dB of insertion loss (IL). Along similar lines,sensor network nodes with much smaller data transfer needs might benefitfrom even smaller channel bandwidths, on the order of only a few kHz,which at 433 MHz would represent only 0.002% bandwidth, for whichresonator Qs on the order of 370,000 would be required!

Meanwhile, though commercial technologies such as FBARs are sufficientfor typical band select usage, the Qs attainable still often limitperformance for narrower band usage. If the Qs could be improved fromthe current values of ˜1000, greater flexibility would be obtained.

Pursuant to achieving the Qs desired for filters, this disclosureexplores the use of active positive feedback to boost the Qs of passiveresonators. In one embodiment presented here, a challenging sub-0.01%bandwidth in a parallel-class filter is demonstrated, though it will beappreciated by one of ordinary skill in the art that the individualQ-boosted resonators may be just as easily used in other filter designs,e.g. mechanically coupled filters.

In one embodiment, the use of active feedback in closed-loop with twoelectrodes of a four-electrode capacitive-gap transduced wine-glass diskresonator has enabled boosting of the effective resonator Q andindependent control of insertion loss across the two other electrodes.

Refer now to FIG. 1, which is a schematic 100 of a Q-boosted parallelfilter comprised of two independent wine-glass disk resonator andamplifier circuits (otherwise referred to as Q-boosted resonators 200),all in a typical measurement circuit.

As a first demonstration of the capability of this approach, two suchQ-boosted resonators 200 are wired in the parallel-type micromechanicalfilter of FIG. 1, to achieve a tiny 0.001% bandwidth passband centeredaround 61 MHz with only 2.7 dB of insertion loss-something not otherwiseknown to be possible with the intrinsic resonator Q of 60,000, but quitepossible with Qs actively boosted to 670,000. Unlike past effortsoperating at kHz-frequencies, the split electrode design used hereremoves the amplifier feedback loop from the signal path allowingindependent control of input-output coupling, Q, and frequency.

Generally speaking, an input signal V_(IN) 102 has an input resistanceR_(Q,in) 104, which is connected to a transformer 106 primary 108. Thetransformer 106 primary 108 is coupled to the center tap 110 of thetransformer 106 positive polarity connection 112 and negative polarityconnection 114.

It is recognized that the balanced input signal V_(IN) 102 is passingthrough essentially a balun to form differential inputs to the Q-boostedresonators 200. However, the differential inputs may be formed insteadby a differential amplifier, an antenna, or just single-ended ordifferential signals directly applied to the Q-boosted resonators 200.

The Q-boosted resonators 200 act to filter the positive polarityconnection 112 and negative polarity connection 114 signals, and arereconnected at the Q-boosted resonators 200 to form a Q-boosted filteroutput V_(OUT) 116, that is characterized by standard test connection ofi_(out) 1118 into a load R_(Q,out) 120.

II. Q and Insertion Loss Adjustable Resonator

Refer now to FIG. 2A through FIG. 2C, which present details of theQ-boosted resonator sub-circuit used twice in the filter circuit ofFIG. 1. FIG. 2A is a detailed schematic 202 of an active Q-boostedresonator 200. A wine-glass resonator 204 is anchored 206, 208, 210, and212 to a substrate (not shown here for the sake of clarity). Thewine-glass resonator 204 is biased via voltage V_(p) 214 through anchor208. Electrodes 216, 218, 220, and 222 capacitively couple to wine-glassresonator 204 to provide input electrode 216, output electrode 218, andclosed loop feedback electrodes 222 and 220 via a transimpedanceamplifier 224. The transimpedance amplifier acts to transform an inputcurrent i_(in, amp) 226 into an amplified output voltage V_(out,amp)228.

An input voltage V_(in) 230 with source impedance R_(Q,in) 232 may befed directly to input electrode 216 (also labeled as port 1). The inputvoltage V_(in) 230 may also be biased with a bias voltage V_(E1) 234that may be coupled through an RC network 236.

The output electrode 218 (also labeled as port 2) may also produce anoutput current i_(out) 238 fed directly to output load R_(Q,out) 240.The output voltage V_(out) 242 may also be biased with a bias voltageV_(E2) 244 that may be coupled through an LC network 246.

FIG. 2B shows the active Q-boosted resonator 200, which largely includesthe microelectromechanical system (MEMS) wine-glass resonator 204,anchors 206, 208, 210, and 212, electrodes 216, 218, 220, and 222, andclosed loop feedback 222 and 220 via a gain and phase-controllabletransimpedance amplifier (TIA) 224.

The active Q-boosted resonator 200 essentially combines a wine-glassdisk resonator 204 with a TIA 224. The wine-glass resonator 204 is inone embodiment constructed from a 2 μm-thick, 32 μm-radius polysilicondisk supported at quasi nodal points by four anchors 206, 208, 210, and212 and surrounded by electrodes 216, 218, 220, and 222 spaced only 65nm 248 from its edges.

Refer back to FIG. 2A. To excite the wine-glass resonator 204 intomotion, a bias voltage V_(P) 214 is applied to the wine-glass resonator204 and an ac drive voltage V_(in) 230 to an input electrode 216. Thesevoltages combine to produce a force across the inputelectrode-to-resonator gap 248 (here about 65 nm) that at resonance canexcite a wine-glass (i.e., compound (2, 1)) vibrational mode shape 250,shown in FIG. 2C, that demonstrates the expansion and contraction of thewine-glass resonator 204 along orthogonal axes.

The expression for resonance frequency takes the form:

$\begin{matrix}{f_{nom} = {\frac{K}{R}\sqrt{\frac{E}{\rho\left( {2 + {2\sigma}} \right)}}}} & (1)\end{matrix}$where R is the disk radius, K=0.373 for a polysilicon structuralmaterial, and E, σ, and ρ are the Young's modulus, Poisson ratio, anddensity of the structural material, respectively.

Once vibration ensues, voltages across the electrode-to-resonator gaps248 generate currents that then serve as electrical input/output (I/O)signals at ports 1 (electrode 216) and 2 (electrode 218) respectively;and as feedback control signals at ports 3 (electrode 222) and 4(electrode 220) conditioned by the transimpedance amplifier 224connected to these ports.

In the circuit of FIG. 2A, the transresistance gain of the TIA 224 addsor subtracts from the damping of the resonator to yield a totaleffective damping (and thus, Q) controllable up or down via the gain andphase of the transimpedance amplifier 224. If the transimpedanceamplifier 224 gain and phase are configured to realize positive feedbackwith loop gain less than unity, then from feedback terminals 1(electrode 216) and 2 (electrode 218) the device looks like anelectrical resonator sporting a bandpass biquad transfer function likeany other electrical resonator, except with extremely high Q on theorder of millions. As such, its small-signal circuit model derivesprincipally from a core LCR tank.

A Q-controlled resonator may comprise: (a) a microelectromechanicalsystem (MEMS) resonant structure; (b) at least four electrodes coupledto the MEMS resonant structure; (c) wherein the MEMS resonant structureis configured to be biased by a tuning voltage V_(P) relative to aground; (d) wherein the four electrodes comprise: (1) an input electrodebiased at V_(E1) relative to the ground; (2) an output electrode biasedat VE₂ relative to the ground; (3) a feedback input electrode; and (4) afeedback output electrode; (d) wherein the MEMS resonant structure has aresonant frequency that is changed by varying the tuning voltage V_(P);and (e) an amplifier, disposed between the feedback input electrode andthe feedback output electrode, configured to form a feedback loop withthe MEMS resonant structure; (f) wherein the feedback loop is configuredto either increase or decrease an intrinsic Q of the MEMS resonantstructure.

A Q-controlled resonator may also comprise: (a) a microelectromechanicalsystem (MEMS) resonant structure; (b) at least four electrodes coupledto the MEMS resonant structure; (c) wherein the four electrodescomprise: (1) an input electrode biased at V_(E1) relative to theground; (2) an output electrode biased at V_(E2) relative to the ground;(3) a feedback input electrode; and (4) a feedback output electrode; (d)wherein the MEMS resonant structure has a resonant frequency that ischanged by varying any of the voltages V_(E1) and V_(E2); and (e) anamplifier, disposed between the feedback input electrode and thefeedback output electrode, configured to form a feedback loop with theMEMS resonant structure; (f) wherein the feedback loop is configured toeither increase or decrease an intrinsic Q of the MEMS resonantstructure.

A. Resonator-Amplifier Electrical Model

Refer now to FIG. 3, which is a detailed schematic 300 of the activeQ-boosted resonator 200 of FIG. 2A through FIG. 2C. To help quantify theQ attainable, FIG. 3 shows the complete small signal model of the FIG.2A and FIG. 2B active Q-boosted resonator device, using a multi-portnegative capacitance resonator equivalent circuit. Here, C_(in) 302,C_(out) 304, C_(ain) 306, and Caout 308 represent capacitance derivedfrom both: 1) intrinsic electrode-to-resonator capacitors; and 2) fromparasitic capacitors surrounding the resonator structure, e.g., fromwire bonding pads. In the resonator model, the values of the core LCRmodel are:

$\begin{matrix}{{r_{x} = c_{mre}},{1_{x} = m_{mre}},{c_{x} = {1\text{/}k_{mre}}}} & (2)\end{matrix}$where c_(mre) 310, m_(mre) 312, and k_(mre) 314 are the mechanicaldamping, mass, and stiffness of the resonator, respectively, determinedelsewhere. In this circuit, variable negative shunt-shunt feedbackresistor R_(F) 316 operates to control the gain G_(m) of thetransimpedance amplifier 318 in conjunction with R_(aout) 320.

The four capacitive-gap electrodes in FIG. 2A and FIG. 2B equate to fournegative capacitor-transformer pairs, with element values of:

$\begin{matrix}{C_{oen} = {{\frac{ɛ_{0}A_{on}}{d_{0}}\mspace{14mu}{and}\mspace{14mu}\eta_{en}} = {V_{PEn}\frac{\partial C}{\partial r}}}} & (3)\end{matrix}$where A_(on) is the static electrode-to-resonator overlap area of then^(th) electrode, d_(o) is the electrode-to-resonator gap spacing(assumed the same for all electrodes), ∂C/∂r is the change inresonator-to-electrode capacitance per unit radial displacement, andV_(PEn) is the DC voltage across the gap of the n^(th) electrode: forinstance, V_(PE1)=V_(P)−V_(E1) for port 1 (electrode 216) in FIG. 2A andFIG. 2B.

Still referring to FIG. 3, by connecting a transimpedance amplifier 318with transconductance G_(m) and output resistance R_(aout) 320, innegative shunt-shunt feedback through R_(F) 316 gives a total impedancelooking into the amplifier of:

$\begin{matrix}{{Z_{amp} = \frac{{- R_{F}}A_{v}\omega_{in}\omega_{out}}{s^{2} + {\left( {\omega_{in} + \omega_{out}} \right)s} + {\omega_{in}{\omega_{out}\left( {1 + A_{v}} \right)}}}}{where}} & (4) \\{{{\omega_{in} = \frac{1}{R_{F}C_{ain}}},{\omega_{out} = \frac{1}{\left( {R_{F}\text{//}R_{aout}} \right)C_{aout}}},{and}}{A_{v} = {G_{m}\left( {R_{F}\text{//}R_{aout}} \right)}}} & (5)\end{matrix}$

Refer now to FIG. 4, which is a graph 400 of theoretically predictedreactance 402 (solid line) and resistance 404 (dashed line) of theimpedance, Z_(amp), looking into the transimpedance amplifier (318 ofFIG. 3) as the feedback resistor, R_(F) (316 of FIG. 3), increases inresistance. Here, approximate representative resistance and capacitancevalues for the transimpedance amplifier in this disclosure are used forsimulation.

As previously stated, FIG. 4 graphs theoretically predicted reactance402 (solid line) and resistance 404 (dashed line) of the impedance,Z_(amp), looking into the TIA amplifier (318 of FIG. 3). However, onlythe real (resistive) part of Z_(amp) (the dashed line) influences thetotal effective damping of the resonator, which with this influencebecomes:c _(eff) =c _(mre) +R _(amp)η_(e3)η_(e4)  (6)

The resultant effective Q then takes the form

$\begin{matrix}{Q_{eff} = \frac{k_{mre}}{\omega_{0}c_{eff}}} & (7)\end{matrix}$which is directly controllable (up or down) via R_(F) (316 of FIG. 3).Clearly, Q_(eff) is larger than the intrinsic Q of the device whenR_(amp) is negative and Q_(eff) is smaller when R_(amp) is positive, andthe transition occurs at point B 406 in FIG. 4, when:

$\begin{matrix}{R_{F} = \frac{G_{m}}{C_{in}C_{out}\omega_{0}^{2}}} & (8)\end{matrix}$

The maximum Q_(eff) occurs at point A 408 in FIG. 4, while the minimumoccurs at point C 410. It is important to note that c_(eff) (of Equation6) must be greater than zero for the system to be stable. This meansthat the loop gain, T, of the feedback loop must satisfy:

$\begin{matrix}{T = {\frac{- R_{{amp},\min}}{R_{x\; 34}} = {\frac{- R_{{amp},\min}}{c_{mre}\text{/}\eta_{e\; 3}\eta_{e\; 4}} = {{1 - \frac{Q_{int}}{Q_{eff}}} < 1}}}} & (9)\end{matrix}$where R_(x34) is the motional impedance looking into electrodes 3 and 4,and Q_(int) is the intrinsic Q of the resonator. In practice, the loopgain T should not be too close to unity, lest some unexpected variation,e.g., noise, acceleration, bumps it past 1, after which uncontrolledoscillation would ensue. Thus, stability considerations will likelylimit the amount of Q-boost in practical design to less than 100 timesthat of the basic resonator.

B. Amplifier-Derived Frequency-Pulling

Refer back to FIG. 2A. During operation, the gap spacing betweenresonator and electrode changes (for instance gap 246), which in turngenerates a changing electric field, and hence varies the electrostaticforce in the gap 246. In a small-signal model, this force is in phaseand proportional to disk edge displacement, and thus meets thedefinition of stiffness. Popularly termed electrical stiffness, this“softens” the equivalent stiffness of the resonator resulting in anegative shift in the resonance frequency. The resultant electricalstiffness generated from the gaps at port 3 and port 4 (respectivelyelectrodes 222 and 220) is:

$\begin{matrix}{k_{e\; 34} = {\eta_{e\; 3}{\eta_{e\; 4}\left\lbrack {\frac{1}{C_{{oe}\; 3}} + \frac{1}{C_{{oe}\; 4}} + {\omega_{0}X_{amp}}} \right\rbrack}}} & (10)\end{matrix}$which subtracts from the wine-glass resonator's 204 mechanical stiffnessto yield a resonance frequency f₀ given by:

$\begin{matrix}{f_{0} = {f_{nom}\sqrt{\left\lbrack {1 - \frac{k_{e\; 1} + k_{e\; 2} + k_{e\; 34}}{k_{mre}}} \right\rbrack}}} & (11)\end{matrix}$where k_(e1) and k_(e2) are the effective electrical stiffnesses fromthe gap at port 1 and 2, respectively (with ports 1 and 2 respectivelylabeled as electrodes 216 and 218).

C. Transimpedance Amplifier Design

Refer now to FIG. 5A, which is a detailed transimpedance amplifier 500circuit comprising a fully differential CMOS transimpedance amplifier502 with one end connected in shunt-shunt feedback to V_(IN) 504, andoutput 506 taken from the other end to realize a 0° input-output phaseshift. Transistor M_(RF) 508 serves as the voltage controllableshunt-shunt feed-back resistor, allowing easy adjustment oftransimpedance amplifier 502 gain via its gate voltage V_(GAIN) 510.

Transistors M1-M4 (respectively 512, 514, 516, and 518) form the basicdifferential transistor pair biased by a common-mode feedback (CMFB)circuit 520 that preserves low output resistance and cancels outcommon-mode noise, including noise caused by vibration. The action ofthe CMFB circuit 520 symmetrically balances the differential paircircuit. This yields a transconductance gain (G_(m)) of 0.5 g_(m1) andoutput resistance (R_(aout)) of approximately r_(o2)//r_(o4), whereg_(m) and r_(o) are transconductance and output resistance of atransistor respectively. The MOS transistor M_(RF) 508 is biased in thetriode region to serve as a voltage controllable shunt-shunt feedbackresistor (R_(F)) that allows convenient adjustment of the TIA gain viaits gate voltage, V_(GAIN) 510.

Refer now to FIG. 5B, which is a photomicrograph of the fabricatedamplifier application specific integrated circuit 522. Here, theamplifier integrated circuit 524 was fabricated in a 0.35 μm CMOStechnology. Although the entire die, shown in FIG. 5B, occupies an areaof 900 μm×500 μm, the actual sustaining amplifier 524 only consumesabout 60 μm×60 μm. The rest of the area is consumed by 1) an on-chipbuffer 526 used to drive 50Ω measurement systems; 2) by-pass capacitors528 further reduce noise on DC supply lines; and 3) bond pads 530.

Though the embodiment demonstrated herein uses a transimpedanceamplifier, it should be appreciated that many other amplifier topologiesmay be substituted. Indeed, any two-port amplifier can create the gainbetween input and output needed to achieve the Q-boosting described.Furthermore, an approach such as a negative-resistance amplifier couldlikewise provide the gain needed to achieve the Q control when connectedto a single resonator port.

Refer now to FIGS. 5C and 5D, which describe the performance of thesystem of FIG. 5A. FIG. 5C is a graph of gain versus frequency of thedevice of FIG. 5A. Similarly, FIG. 5D is a graph of phase versusfrequency of the device of FIG. 5A.

III. Active Q-Boosted Filter Implementation

Refer now to FIG. 1 once again. To create a filter response, the circuitof FIG. 1 combines into a parallel-class filter similar to that of twoFIG. 2A electromechanical circuits with resonance frequencies spacedfrom one another by the desired passband bandwidth. A balun 102 convertsa single ended input 104 at the left into a differential drive signalwith plus end applied to one active Q-controlled resonator 200 input andminus to the other, so that each active Q-controlled resonator 200receives oppositely phased inputs. The output terminals of each of thetwo active Q-controlled resonators 200 are then tied together so thattheir output currents add to form i_(out) 108.

In this approach, the filter response is achieved via electricallycombining the signals from both resonators. As with any mechanicalfilter, a filter response may equally be created by mechanicallycoupling the resonators via a coupling beam. In such a design, the beamforces the frequencies of the individual resonators to separate,creating a passband in the mechanical response directly.

Refer now to FIG. 6A, which is a graph 600 of transmission versusfrequency of parallel filter operation, where two differentially drivenbandpass biquad responses add to form a flat passband (between thepeaks) and subtract in the stopband (outside the peaks) to providegreater stopband rejection.

Here, the individual resonator spectra of Q-boosted resonator 1 602 andQ-boosted resonator 2 604 operationally combine together to form theresulting filter spectrum 606, with flat passband 608.

Refer now to FIG. 6B, which is a graph 610 of phase versus frequency ofthe parallel Q-boosted filter operation modeled in FIG. 6A. As shown,the differential drive of the resonator 1 612 and resonator 2 614produces a relative phase shift of approximately 0° in the passband 608,which allows their outputs to add to 616 form a flat filter passbandbetween these peaks. Meanwhile, outside the passband the resonatorsvibrate 180° out-of-phase, giving rise to subtraction that steepens theroll-off of the stopband.

A. Adjustable Dynamic Range

Refer now back to FIG. 2A. As with any bandpass filter, the higher the Qof the constituent resonators, the lower the insertion loss. This meansthe insertion loss of the filter should be fully controllable by merelyadjusting the gain of the Q-boosted transimpedance amplifiers 224 placedin feedback between ports 3 and 4 (electrodes 222 and 220 respectively)of each active Q-boosted resonator 200.

Refer now to FIG. 7A, which is a graph 700 of transmission versusfrequency of the simulations of FIG. 1. Here are presented simulatedparallel filter responses for a narrow 0.002% bandwidth filter with lowQ (intrinsic device Q) equivalent to 1.36×BW_(fil) 702, Q-boosted by twotimes 704, and Q-boosted by 22 times 706. These curves show responsesfor constant R_(Q) (the value needed to approximate an equivalentresistive insertion loss R_(Q) for the highest Q case) and insertionloss improvement of 12 dB, which is the difference between the highesttransmission of the 1.36×BW_(fil) 702 curve and the Q-boosted by 22times 706 curve.

Refer now to FIG. 7B, which is a graph 708 that illustrates that thefilter can be terminated properly by adjusting the bias voltage acrossinput and output gaps while R_(Q) is kept constant. Note that the Qequivalent to 1.36×BW_(fil) 710 is too small for the filter to beterminated properly. Boosting Q by 2 times 712 improves the insertionloss by about 12 dB. Boosting Q by 22 times in curve 714 improvesinsertion loss by about 23 dB.

Referring now to both FIG. 7A and FIG. 7B, it appears that activeQ-control not only makes possible low insertion loss even for 0.002%bandwidth filters that would not be feasible otherwise, but also enablesvariable gain filters, as opposed to the variable gain low noiseamplifiers commonly used in radio frequency front-ends.

The curves in FIG. 7A lose their passband shape as Q is lowered, mainlybecause the motional resistance of the constituent active Q-boostedresonators 200 change with their Q, so the R_(Qs) no longer present theneeded termination. To remedy this, the electrode-to-resonator DC-biasvoltages V_(E1) (234 of FIG. 2A) and V_(E2) (242 of FIG. 2A) can beadjusted to compensate, which then yields the curves of FIG. 7B, wherethe filter frequency response retains its shape even as insertion lossesincrease.

The ability to tune insertion loss essentially amounts to an ability toadjust dynamic range. In particular, if the input to the filter receivesa signal sufficiently high in amplitude to drive it into nonlinearbehavior, one need only tune the Q-controlling amplifier gain toincrease insertion loss, thereby allowing reception of the signalwithout desensitization. In effect, this adjustable insertion lossprovides an effective bias shift for dynamic range—a very usefulfunction for any transceiver front-end.

B. Power Consumption Considerations

The use of active circuits in an otherwise passive filter implementationdoes introduce power consumption, where there was none before. The extraactive circuits are justified only if their presence offers performancebenefits beyond what might be achieved by raising power consumptionelsewhere in the system, e.g., in the low noise amplifier orintermediate frequency channel-select filter (if realized usingtransistors). In fact, typical low noise amplifier power consumption ison the order of 5 mW, which is needed mainly to insure an adequate noisefigure. Recent developments in passive transformer coupled front-endshave successfully reduced the power consumption in the low noiseamplifier and mixer close to zero, but due to the lack of radiofrequency channel-select filtering in traditional technologies, power onthe order of 10 mW is still needed to maintain adequate linearity in theactive intermediate frequency channel-select filter.

Meanwhile, the power required for the active circuits in the Q-boostingloop in the active Q-boosted resonator 200 of FIG. 2A can be sub-100 μW,making the Q-boosted MEMS approach more desirable from a powerconsumption standpoint. This argument becomes even more important withthe recognition that the loss of a radio frequency front-end filterdirectly adds to the noise figure of a receiver, so lowering radiofrequency filter insertion loss by several dB is often a betterinvestment of consumed power than lowering the noise figure of a lownoise amplifier by a smaller dB number.

IV. Experimental Results

Refer now to FIG. 8A through FIG. 8C. To experimentally verify theutility of active Q-boosting, wine-glass resonators were designed andfabricated with a process summarized in the cross sections of FIG. 8Aand FIG. 8B.

FIG. 8A is a cross section 800 illustrating one embodiment of a MEMSresonator prior to resonator disk release in 49% HF. Here, dopedpolysilicon serves as the structural material for resonator 802 andelectrodes 804, alike, and the gaps 806 between the resonator 802 andelectrodes 804 were set at 65 nm by a sacrificial high-temperature oxidespacer 808 that is removed in the final release step. The processdiffers from previous ones in that it removes electrode overhangs viachemical mechanical planarization (CMP)—a step that improves thereliability of devices under larger DC-bias voltages. An additionalsacrificial hard mask 810 protects the top surface of the resonator 802during some of the etching procedures.

FIG. 8B shows the cross section 812 of FIG. 8A, where the sacrificialhigh-temperature oxide spacer 808 (of FIG. 8A) and the additionalsacrificial hard mask 810 (also of FIG. 8A) have both been removed.

FIG. 8C presents a scanning electromicrograph SEM of a fabricated device814 of FIG. 8B following release in 49% HF. The device here has a radiusof 32 μm, electrode-to-resonator gap spacing of 65 nm, and DC-biasvoltage V_(P) of 10 V. This fabricated device provides a couplingstrength of (C_(x)/C_(o)) ˜0.04% at an operating frequency of 61 MHz,sufficient for the 0.001% bandwidth filter demonstrated here.

Refer now to FIG. 9A, which is a graph 900 of transmission versusfrequency for single resonator Q-boosting as a function of amplifiergain with constant V_(P)=8.5 V. These curves (902, 904, 906, 908, 910,912, and 914) present measured electrical transmission plots for a50Ω-terminated single disk resonator in a Q-controlling hookup (cf. FIG.2A) as a function of transimpedance gain and phase shift. Here,insertion loss and Q are quite tunable, with effective Q adjustableanywhere from 24 k to 2.3M. Even operating at the maximum boosted Q of2.3M, the active resonator remained stable for hours of measurement timewith no evidence of oscillation, likely a result of compactimplementation made possible by die-level ASIC and MEMS resonatorconnections previously described in FIG. 5B.

The curves of FIG. 9A also confirm that the resonance frequency shiftsto the left with decreasing V_(GAIN).

Refer now to FIG. 9B, which is a graph of transmission versus frequency916 that further demonstrates insertion loss tuning while maintainingconstant Q (by keeping V_(GAIN) constant) via independent tuning of theinput-output electrode to disk bias voltage, i.e., tuning V_(E1) andV_(E2).

As V_(GAIN) is decreased amplifier gain increases, boosting effectiveresonator Q (902, 904, and 906 of FIG. 9A) from an initial intrinsicQ=57,000 to a maximum boosted Q of 2.3 million (908). On the other hand,decreasing V_(GAIN) further allows control of amplifier phase shift,leading to negative feedback and allowing controlled loading of Q (910,912, and 914 of FIG. 9A).

Refer now to FIG. 9B, which is a graph 916 of the transmission versusfrequency of a single resonator Q-boosting device. This set of curves918, 920, and 922 demonstrates independent tuning of frequency andinsertion loss via control of the voltage across input-outputelectrode-disk gap, all while holding Q constant by holding V_(GAIN)constant.

FIG. 10 is a graph 1000 of Quality Factor (Q) versus gain controllingvoltage. Here, measured effective quality factor 1002 and insertion loss1004 of the resonator with constant V_(P)=8.5 V as V_(GAIN) of theamplifier changes. The highest Q and lowest insertion loss occur at alittle over 2.495 V 1006.

Refer now to FIG. 11A, which is a graph 1100 of measured transmissionversus frequency for a two-resonator active Q-boosted resonator 200arranged in a circuit as shown in FIG. 1, and terminated by the designed(i.e., required) value of 1.7 kΩ at both input and output for the caseswith 1102 and without 1104Ω-boosting transimpedance amplifiers.

Refer now to FIG. 11B, which is a graph 1106 of the group delay in msversus frequency of the device previously shown in FIG. 11A in curve1102. In both FIGS. 11A and 11B, the device parameters used weref0=60.5376 MHz, BW-600 Hz, IL=2.7 dB, RJ=30 dB, V_(P1)=13.4 V, GroupDelay=0.7 ms, R_(Q)=1.7 kΩ, Ripple=0.3 dB, SF20 dB=2.55, and V_(P2)=16.5V.

As expected, the insertion loss is a dismal 21 dB without Q-boosting ofthe constituent resonators (see curve 1104 of FIG. 11A); compared withonly 2.7 dB when the transimpedance amplifiers boost Qs (see curve 1102of FIG. 11A). Indeed, 2.7 dB is quite impressive for a percentagebandwidth this small.

Refer back again to FIG. 10 to verify the theoretical predictions ofFIG. 4. Here, FIG. 10 additionally demonstrates the Q enhancement andsubsequent improvement in insertion loss when measured with 50Ωterminations as a function of V_(GAIN) applied to the amplifier. AsV_(GAIN) decreases, the shunt-shunt feedback resistance R_(F) in thetransimpedance amplifier increases.

As previously depicted in FIG. 4, with increasing R_(F), R_(amp)(initially a negative value and hence boosting Q) decreases to a minimumvalue for the maximum Q of 2.3M and the maximum loop gain of 0.975.Decreasing V_(GAIN) further decreases Q (or increases R_(amp)) until itbecomes smaller than the resonator intrinsic Q at which point R_(amp) isgreater than zero.

On the other hand, the stopband rejection of only 30 dB seen in FIG. 11Ais less than expected. The insufficient stopband rejection actuallyderives from the measurement apparatus and scheme, not the deviceitself. In particular, the current measurement simulates the neededfilter terminations using network analyzer-based load simulation, ratherthan a real 1.7 kΩ termination impedance, and this compromises the noisefloor of the instrument. An improved measurement effort using realterminations, currently underway, is expected to improve this lowrejection measurement artifact.

V. Conclusions

The demonstration in this disclosure of a 0.001% bandwidthmicromechanical filter comprised of actively Q-boosted passiveresonators with only 2.7 dB of insertion loss is thought to be the firstof its kind on the micro-scale, and presents opportunities forimplementing some very unique and desired capabilities in the nearfuture. Opportunities to realize radio frequency channel-selectingradios were the focus of this disclosure, and the demonstrated Qs up to2.3 million should prove very useful towards greatly lowering powerconsumption for the low data rate wireless communications needed fornetwork sensors. Bandwidths as small as 0.001% might further enablenoise shaping for oscillators and other applications to unprecedentedperformance marks.

Although this work focused on very small percent bandwidth filters, itis worthwhile to reconsider use of these techniques in more mainstreamapplications, like cellular communications, for which RFchannel-selection still offers substantial reductions in powerconsumption. As previously mentioned, existing resonator technologies donot yet possess the simultaneous Q and coupling characteristics orealize such a front-end. As described in this disclosure, as long asthe small additional power consumption is acceptable, active Q-boostingmight be a good answer for resonators that possess adequate coupling,but insufficient Q.

In other words, RF channel-selection for piezoelectric resonators mayindeed just be a few more electrodes and some active circuits away fromreality, especially for piezoelectric resonators that start with decentQs, e.g., ones using capacitive-piezo transducers, or composite materialstructures.

One of ordinary skill in the art will appreciate that the methodspresented herein are widely applicable to a range of resonator deviceswhich utilize a capacitive gap/coupling/transducer for transduction.Furthermore, the techniques are also applicable to resonators which arenot typically actuated through this capacitive gap (e.g., piezo coupleddevices). Accordingly, the disclosed teachings are applicable to a rangeof resonators, given by way of example and not limitation as: ringresonators (both contour mode or others, such as wine-glass ring), Lamemode resonators, bar resonators, flexural beam resonators, membrane or“drum head” resonators, comb-driven flexural-mode resonators withsuitable tuning electrodes, center-supported disk resonators (e.g.,using both in-plane contour, and whispering gallery modes, or variousflexural mode operation), surface acoustic wave (SAW) devices, bulkacoustic wave (BAW) devices, film bulk acoustic resonator (FBAR)devices, lateral overmoded bulk acoustic-wave resonator (LOBAR) devices,or other piezo actuated resonators. Additionally, internal dielectricactuated resonators may be utilized in any of the above mode shapes,where the needed capacitive coupling is provided by the internaldielectric gap. Similarly, internally-transduced resonators, may beutilized in which the capacitive-gap is formed from a semiconductorjunction, as in body-resonator transistors. Still further, the disclosedteachings may be utilized with various combinations of the above deviceswithout departing from these disclosed teachings.

Note also that though the described embodiment here demonstrates atwo-resonator filter, higher-order filters may also be constructed frommore than two individual Q-controlled resonators. From the perspectiveof filter design, these Q-controlled MEMS resonator elements behaveexactly as passive resonators, affording all the variations on designpossible with passive resonators.

Refer now to FIG. 12, which is a variant 1200 of the Q-boosted filterwhere multiple resonators 200 may be Q-boosted using a single amplifier1202. Here, a positive input signal V_(in+) 1204 is input into a firstQ-boosted resonator 200 at input electrode 1206, and a negative inputsignal V_(in−) 1206 is input into a second Q-boosted resonator 200 atinput electrode 1208. By wiring the input of the amplifier 1202 tofeedback electrodes 1212, 1214 on both Q-boosted resonators 200, and thelikewise wiring the amplifier 1202 output to feedback electrodes 1216,1218 on each Q-boosted resonators 200 simultaneously, Q boosting isachieved for both resonators, while reducing the total power consumptionthat would otherwise be consumed with the use of multiple amplifiers.

This single amplifier 1202 approach additionally exposes both resonatorsto the same noise from the amplifier (i.e., coherent noise). As aresult, when the signal is combined from output electrode 1220, 1222 toform output current i_(out) 1224 into output load R_(Q,out) 1226, thecomparative phase response of the resonators in the passbands cancelsthis noise, providing a filter with, at least theoretically, no addednoise from the process of Q-boosting resonators. Of course, thisapproach may also be expanded to mechanically coupled filters andfilters using more than two resonators operating on a single amplifier.

From the description herein, it will be appreciated that that thepresent disclosure encompasses multiple embodiments which include, butare not limited to, the following:

1. A Q-boosted filter, comprising: (a) a first Q-boosted resonator, saidfirst Q-boosted resonator comprising: (i) a resonant structure; (ii) aninput electrode, an output electrode, and one or more feedbackelectrodes, each of said electrodes coupled to the resonant structure;(iii) an amplifier, disposed between two or more feedback electrodesthat is configured to form a feedback loop with the resonant structure;(iv) wherein the gain and phase shift of the amplifier may be controlledto change an intrinsic Q of the resonant structure; (b) a secondQ-boosted resonator, said second Q-boosted resonator comprising: (i) aresonant structure; (ii) an input electrode, an output electrode, andone or more feedback electrodes, each of said electrodes coupled to theresonant structure; (iii) an amplifier, disposed between two or morefeedback electrodes configured to form a feedback loop with the resonantstructure; (iv) wherein the gain and phase shift of the amplifier may becontrolled to change an intrinsic Q of the resonant structure; (v)wherein the positive feedback loop is configured to boost an intrinsic Qof the resonant structure; and (c) a differential input signalcomprising: (i) a positive polarity connection to the input electrode ofthe first Q-boosted resonator; (ii) a negative polarity connection tothe input electrode of the second Q-boosted resonator; (d) wherein theoutput electrode of the first Q-boosted resonator and the outputelectrode of the second Q-boosted resonator are connected together toprovide a Q-boosted filter output.

2. The Q-boosted filter of any preceding embodiment, wherein each saidresonant structure is selected from a group of resonators consisting of:comb-driven resonators, piezo coupled resonators, ring resonators,contour mode ring resonators, wine-glass ring resonators, Lame moderesonators, bar resonators, flexural beam resonators, membraneresonators, comb-driven flexural-mode resonators, center-supported diskresonators, surface acoustic wave (SAW) devices, bulk acoustic wave(BAW) devices, film bulk acoustic resonator (FBAR) devices, lateralovermoded bulk acoustic-wave resonator (LOBAR) devices, piezo actuatedresonators, internal dielectric actuated resonators,internally-transduced resonators having a capacitive couple formed froma semiconductor junction, and combinations of the foregoing.

3. The Q-boosted filter of any preceding embodiment, wherein thedifferential input signal comprises: (a) an input transformer,comprising: (i) a primary winding; (ii) a secondary winding having agrounded center tap; (iii) the secondary winding having a positivepolarity tap and a negative polarity tap; and (b) wherein an inputsignal connected to the primary winding results in the differentialinput signal produced by the positive polarity tap and the negativepolarity tap.

4. The Q-boosted filter of any preceding embodiment, wherein thedifferential input signal is produced via a differential amplifierproviding a positive polarity and a negative polarity output.

5. A Q-boosted filter, comprising: (a) a first Q-boosted resonator, saidfirst Q-boosted resonator comprising: (i) a resonant structure; (ii) aninput electrode, an output electrode, and one or more feedbackelectrodes, each of said electrodes electromechanically coupled to theresonant structure; (iii) an amplifier, disposed between two or morefeedback electrodes that is configured to form a feedback loop with theresonant structure; (iv) wherein the gain and phase shift of theamplifier may be controlled to increase or decrease an intrinsic Q ofthe resonant structure; and (b) one or more additional Q-boostedresonators, said Q-boosted resonators comprising: (i) a resonantstructure; (ii) an input electrode, an output electrode, and one or morefeedback electrodes, each of said electrodes electromechanically coupledto the resonant structure; (iii) an amplifier, disposed between two ormore feedback electrodes configured to form a feedback loop with theresonant structure; (iv) wherein the gain and phase shift of theamplifier may be controlled to increase or decrease an intrinsic Q ofthe resonant structure; (v) wherein the positive feedback loop isconfigured to boost an intrinsic Q of the resonant structure; and (c)one or more mechanical coupling beams connecting the Q-boosted resonatorstructure; (d) wherein the output electrodes of all Q-boosted resonatorsare connected together to provide a Q-boosted filter output.

6. The Q-boosted filter of any preceding embodiment, wherein each saidresonant structure is selected from a group of resonators consisting of:comb-driven resonators, piezo coupled resonators, ring resonators,contour mode ring resonators, wine-glass ring resonators, Lame moderesonators, bar resonators, flexural beam resonators, membraneresonators, comb-driven flexural-mode resonators, center-supported diskresonators, surface acoustic wave (SAW) devices, bulk acoustic wave(BAW) devices, film bulk acoustic resonator (FBAR) devices, lateralovermoded bulk acoustic-wave resonator (LOBAR) devices, piezo actuatedresonators, internal dielectric actuated resonators,internally-transduced resonators having a capacitive coupled formed froma semiconductor junction, and combinations of the foregoing.

7. The Q-boosted filter of any preceding embodiment, wherein thedifferential input signal comprises: (a) an input transformer,comprising: (i) a primary winding; and (ii) a secondary winding having agrounded center tap; (iii) the secondary winding having a positivepolarity tap and a negative polarity tap; and (b) wherein an inputsignal connected to the primary winding results in the differentialinput signal produced by the positive polarity tap and the negativepolarity tap.

8. The Q-boosted filter of any preceding embodiment, wherein thedifferential input signal is produced via a differential amplifierproviding a positive polarity output and a negative polarity output froma balanced input signal.

9. A Q-boosted filter, comprising: (a) a first Q-boosted resonator, saidfirst Q-boosted resonator comprising: (i) a resonant structure; (ii) aninput electrode, an output electrode, a feedback input electrode, and afeedback output electrode, each of said electrodes coupled to theresonant structure; (iii) wherein the resonant structure is configuredto be biased by a tuning voltage relative to the input electrode, theoutput electrode, the feedback input electrode, and the feedback outputelectrode; (iv) wherein the resonant structure has a resonant frequencythat is changed by varying the tuning voltage; and (v) an amplifier,disposed between the feedback input electrode and the feedback outputelectrode, that is configured to form a positive feedback loop with theresonant structure; (vi) wherein the positive feedback loop isconfigured to boost an intrinsic Q of the resonant structure; (b) asecond Q-boosted resonator, said second Q-boosted resonator comprising:(i) a resonant structure; (ii) an input electrode, an output electrode,a feedback input electrode, and a feedback output electrode, each ofsaid electrodes coupled to the resonant structure; (iii) wherein theresonant structure is configured to be biased by a tuning voltagerelative to the input electrode, the output electrode, the feedbackinput electrode, and the feedback output electrode; (iv) wherein theresonant structure has a resonant frequency that is changed by varyingthe tuning voltage; and (v) an amplifier, disposed between the feedbackinput electrode and the feedback output electrode, that is configured toform a positive feedback loop with the resonant structure; (vi) whereinthe positive feedback loop is configured to boost an intrinsic Q of theresonant structure; and (c) an input transformer, comprising: (i) aprimary winding; (ii) a secondary winding having a grounded center tap;(iii) the secondary winding having a positive polarity connection to theinput electrode of the first Q-boosted resonator; (iv) the secondarywinding having a negative polarity connection to the input electrode ofthe second Q-boosted resonator; (d) wherein the output electrode of thefirst Q-boosted resonator and the output electrode of the secondQ-boosted resonator are connected together to provide a Q-boosted filteroutput.

10. The Q-boosted filter of any preceding embodiment, wherein an inputsignal connected to the primary winding results in the Q-boosted filteroutput.

11. The Q-boosted filter of any preceding embodiment, wherein electrodecoupling is selected from a group of couplings consisting of: capacitiveand piezo-electric.

12. The Q-boosted filter of any preceding embodiment, wherein eachresonant structure is a wine-glass disk resonator.

13. The Q-boosted filter of any preceding embodiment, wherein eachresonant structure is supported above a substrate by one or moreanchors.

14. The Q-boosted filter of any preceding embodiment, wherein eachresonant structure tuning voltage is transmitted through one or more ofthe anchors.

15. A Q-boosted resonator, comprising: (a) a resonant structure; (b) aninput electrode, an output electrode, a feedback input electrode, and afeedback output electrode, each of said electrodes capacitively coupledto the resonant structure; (c) wherein the resonant structure isconfigured to be biased by a tuning voltage relative to the inputelectrode, the output electrode, the feedback input electrode, and thefeedback output electrode; (d) wherein the resonant structure has aresonant frequency that is changed by varying the tuning voltage; and(e) an amplifier, disposed between the feedback input electrode and thefeedback output electrode, that is configured to form a positivefeedback loop with the resonant structure; (f) wherein the positivefeedback loop is configured to boost an intrinsic Q of the resonantstructure.

16. The Q-boosted resonator of any preceding embodiment, wherein eachamplifier comprises a transimpedance amplifier.

17. The Q-boosted resonator of any preceding embodiment, wherein eachresonant structure is selected from a group of resonators consisting of:comb-driven resonators, piezo coupled resonators, ring resonators,contour mode ring resonators, wine-glass ring resonators, Lame moderesonators, bar resonators, flexural beam resonators, membraneresonators, comb-driven flexural-mode resonators, center-supported diskresonators, surface acoustic wave (SAW) devices, bulk acoustic wave(BAW) devices, film bulk acoustic resonator (FBAR) devices, lateralovermoded bulk acoustic-wave resonator (LOBAR) devices, piezo actuatedresonators, internal dielectric actuated resonators,internally-transduced resonators having a capacitive couple formed froma semiconductor junction, and combinations of the foregoing.

18. The Q-boosted resonator of any preceding embodiment, wherein eachresonant structure is supported above a substrate by one or moreanchors.

19. The Q-boosted resonator of any preceding embodiment, wherein eachresonant structure tuning voltage is transmitted through one or more ofthe anchors.

20. A Q-boosted filter, comprising: (a) a input transformer that couplesa balanced input signal to two unbalanced Q-boosted resonators; and (b)means for filtering, comprising: (i) an input signal connected to theinput transformer through the two unbalanced Q-boosted resonators; and(ii) a filtered output signal formed by a connection of two outputelectrodes on the respective two unbalanced Q-boosted resonators.

21. The Q-boosted filter of any preceding embodiment, wherein eachunbalanced Q-boosted resonator comprises: (a) a resonant structure; (b)an input electrode, the output electrode, a feedback input electrode,and a feedback output electrode, each of said electrodes capacitivelycoupled to the resonant structure; (c) wherein the resonant structure isconfigured to be biased by a tuning voltage relative to the inputelectrode, the output electrode, the feedback input electrode, and thefeedback output electrode; (d) wherein the resonant structure has aresonant frequency that is changed by varying the tuning voltage; and(e) an amplifier, disposed between the feedback input electrode and thefeedback output electrode, that is configured to form a positivefeedback loop with the resonant structure; (f) wherein the positivefeedback loop is configured to boost an intrinsic Q of the resonantstructure.

22. A method of Q-boosted filtering, comprising: (a) providing an inputsignal; (b) splitting the input signal into two signals 180° out ofphase; (c) passing each of the 180° out of phase signals through arespective Q-boosted resonator; and (d) combining each output of theQ-boosted resonators into a Q-boosted filter output.

23. The method of Q-boosted filtering of any preceding embodiment,further comprising: (a) controlling a resonant frequency of eachQ-boosted resonator; (b) wherein a substantially flat pass band isformed between the resonance frequencies of the two Q-boostedresonators.

24. The method of Q-boosted filtering of any preceding embodiment,wherein each Q-boosted resonator comprises: (a) a resonant structure;and (b) an input electrode, the output electrode, a feedback inputelectrode, and a feedback output electrode, each of said electrodescapacitively coupled to the resonant structure.

25. The method of Q-boosted filtering of any preceding embodiment,wherein controlling the resonant frequency for one of the Q-boostedresonators comprises: applying a bias voltage between the resonantstructure of the Q-boosted resonator and the input electrode, the outputelectrode, the feedback input electrode, and the feedback outputelectrode, each of said electrodes capacitively coupled to the resonantstructure.

26. A Q-boosted filter, comprising: (a) a first Q-boosted resonator,said first Q-boosted resonator comprising: (i) a resonant structure; and(ii) an input electrode, an output electrode, and one or more feedbackelectrodes, each of said electrodes coupled to the resonant structure;(b) a second Q-boosted resonator, said second Q-boosted resonatorcomprising: (i) a resonant structure; and (ii) an input electrode, anoutput electrode, and one or more feedback electrodes, each of saidelectrodes coupled to the resonant structure; (c) an amplifier, disposedbetween feedback electrodes of both Q-boosted resonators, configured toform feedback loops with both resonant structures simultaneously; (i)wherein the gain and phase shift of the amplifier may be controlled tochange the Qs of the resonant structures; and (d) a differential inputsignal comprising: (i) a positive polarity connection to the inputelectrode of the first Q-boosted resonator; (ii) a negative polarityconnection to the input electrode of the second Q-boosted resonator; (e)wherein the output electrode of the first Q-boosted resonator and theoutput electrode of the second Q-boosted resonator are connectedtogether to provide a Q-boosted filter output.

27. The Q-boosted filter of any preceding embodiment, wherein each saidresonant structure is selected from a group of resonators consisting of:comb-driven resonators, piezo coupled resonators, ring resonators,contour mode ring resonators, wine-glass ring resonators, Lame moderesonators, bar resonators, flexural beam resonators, membraneresonators, comb-driven flexural-mode resonators, center-supported diskresonators, surface acoustic wave (SAW) devices, bulk acoustic wave(BAW) devices, film bulk acoustic resonator (FBAR) devices, lateralovermoded bulk acoustic-wave resonator (LOBAR) devices, piezo actuatedresonators, internal dielectric actuated resonators,internally-transduced resonators having a capacitive couple formed froma semiconductor junction, and combinations of the foregoing.

28. The Q-boosted filter of any preceding embodiment, wherein thedifferential input signal comprises: (a) an input transformer,comprising: (i) a primary winding; and (ii) a secondary winding having agrounded center tap; (iii) the secondary winding having a positivepolarity tap and a negative polarity tap; (b) wherein an input signalconnected to the primary winding results in the differential inputsignal produced by the positive polarity tap and the negative polaritytap.

29. The Q-boosted filter of any preceding embodiment, wherein thedifferential input signal is produced via a differential amplifierproviding a positive polarity and a negative polarity output from aninput signal.

30. A Q-boosted filter, comprising: (a) a first Q-boosted resonator,said first Q-boosted resonator comprising: (i) a resonant structure; and(ii) an input electrode, an output electrode, and one or more feedbackelectrodes, each of said electrodes electromechanically coupled to theresonant structure; (b) one or more additional Q-boosted resonators,said Q-boosted resonators comprising: (i) a resonant structure; and (ii)an input electrode, an output electrode, and one or more feedbackelectrodes, each of said electrodes electromechanically coupled to theresonant structure; (c) an amplifier, disposed between feedbackelectrodes of both Q-boosted resonators that is configured to formfeedback loops with both resonant structures simultaneously; (i) whereinthe gain and phase shift of the amplifier may be controlled to changethe Qs of the resonant structures; and (d) one or more mechanicalcoupling beams connecting the Q-boosted resonator structure; (e) whereinthe output electrodes of all Q-boosted resonators are connected togetherto provide a Q-boosted filter output.

31. The Q-boosted filter of any preceding embodiment, wherein each saidresonant structure is selected from a group of resonators consisting of:comb-driven resonators, piezo coupled resonators, ring resonators,contour mode ring resonators, wine-glass ring resonators, Lame moderesonators, bar resonators, flexural beam resonators, membraneresonators, comb-driven flexural-mode resonators, center-supported diskresonators, surface acoustic wave (SAW) devices, bulk acoustic wave(BAW) devices, film bulk acoustic resonator (FBAR) devices, lateralovermoded bulk acoustic-wave resonator (LOBAR) devices, piezo actuatedresonators, internal dielectric actuated resonators,internally-transduced resonators having a capacitive couple formed froma semiconductor junction, and combinations of the foregoing.

32. The Q-boosted filter of any preceding embodiment, wherein thedifferential input signal comprises: (a) an input transformer,comprising: (i) a primary winding; and (ii) a secondary winding having agrounded center tap; (iii) the secondary winding having a positivepolarity tap and a negative polarity tap; (b) wherein an input signalconnected to the primary winding results in the differential inputsignal produced by the positive polarity tap and the negative polaritytap.

33. The Q-boosted filter of any preceding embodiment, wherein thedifferential input signal is produced via a differential amplifierproviding a positive polarity output and a negative polarity output froma balanced input signal.

34. A Q-boosted resonator, comprising: (a) a resonant structure; (b) atleast four electrodes coupled to the resonant structure; (c) wherein theresonant structure is configured to be biased by a tuning voltagerelative to the electrode that is an input, the electrode that is anoutput, the electrode that is a feedback input, and the electrode thatis a feedback output; and (d) wherein the resonant structure has aresonant frequency that is changed by varying the tuning voltage; and(e) an amplifier, disposed between the feedback input electrode and thefeedback output electrode, that is configured to form a positivefeedback loop with the resonant structure; (f) wherein the positivefeedback loop is configured to boost an intrinsic Q of the resonantstructure.

35. The Q-boosted resonator of the embodiments above, (a) wherein the atleast four electrodes comprise an input electrode, an output electrode,a feedback input electrode, and a feedback output electrode, each ofsaid electrodes coupled to the resonant structure; and (b) wherein eachof said electrodes is coupled by a coupling selected from a group ofcouplings consisting of: capacitive and piezoelectric.

36. The Q-boosted resonator of the embodiments above, wherein eachamplifier comprises a transimpedance amplifier.

37. The Q-boosted resonator of the embodiments above, wherein eachresonant structure is selected from a group of resonators consisting of:comb-driven resonators, piezo coupled resonators, ring resonators,contour mode ring resonators, wine-glass ring resonators, Lame moderesonators, bar resonators, flexural beam resonators, membraneresonators, comb-driven flexural-mode resonators, center-supported diskresonators, surface acoustic wave (SAW) devices, bulk acoustic wave(BAW) devices, film bulk acoustic resonator (FBAR) devices, lateralovermoded bulk acoustic-wave resonator (LOBAR) devices, piezo actuatedresonators, internal dielectric actuated resonators,internally-transduced resonators having a capacitive couple formed froma semiconductor junction, and combinations of the foregoing.

38. The Q-boosted resonator of the embodiments above, wherein eachresonant structure is supported above a substrate by one or moreanchors.

39. The Q-boosted resonator any of the embodiments above, wherein eachresonant structure tuning voltage is transmitted through one or more ofthe anchors.

Although the description herein contains many details, these should notbe construed as limiting the scope of the disclosure but as merelyproviding illustrations of some of the presently preferred embodiments.Therefore, it will be appreciated that the scope of the disclosure fullyencompasses other embodiments which may become obvious to those skilledin the art.

In the claims, reference to an element in the singular is not intendedto mean “one and only one” unless explicitly so stated, but rather “oneor more.” All structural, chemical, and functional equivalents to theelements of the disclosed embodiments that are known to those ofordinary skill in the art are expressly incorporated herein by referenceand are intended to be encompassed by the present claims. Furthermore,no element, component, or method step in the present disclosure isintended to be dedicated to the public regardless of whether theelement, component, or method step is explicitly recited in the claims.No claim element herein is to be construed as a “means plus function”element unless the element is expressly recited using the phrase “meansfor”. No claim element herein is to be construed as a “step plusfunction” element unless the element is expressly recited using thephrase “step for”.

What is claimed is:
 1. A method of Q-boosted filtering, comprising: (a)providing an input signal; (b) splitting the input signal into twosignals 180° out of phase; (c) passing each of the 180° out of phasesignals through a respective Q-boosted resonator; and (d) combining eachoutput of the Q-boosted resonators into a Q-boosted filter output; (e)wherein each Q-boosted resonator is a microelectromechanical system(MEMS) resonator.
 2. A Q-boosted resonator, comprising: (a) amicroelectromechanical system (MEMS) wine-glass resonant structure; (b)at least four electrodes coupled to the resonant structure; (c) whereinthe resonant structure is configured to be biased by a tuning voltagerelative to the electrode that is an input, the electrode that is anoutput, the electrode that is a feedback input, and the electrode thatis a feedback output; and (d) wherein the resonant structure has aresonant frequency that is changed by varying the tuning voltage; and(e) an amplifier, disposed between the feedback input electrode and thefeedback output electrode, that is configured to form a positivefeedback loop with the resonant structure; (f) wherein the positivefeedback loop is configured to boost an intrinsic Q of the resonantstructure.
 3. The Q-boosted resonator of claim 2: (a) wherein the atleast four electrodes comprise an input electrode, an output electrode,a feedback input electrode, and a feedback output electrode, each ofsaid electrodes coupled to the resonant structure; and (b) wherein eachof said electrodes is coupled by a coupling selected from a group ofcouplings consisting of: capacitive and piezoelectric.
 4. The Q-boostedresonator of claim 2, wherein each amplifier comprises a transimpedanceamplifier.
 5. The Q-boosted resonator of claim 2, wherein each amplifiercomprises a negative-resistance amplifier.
 6. The method of Q-boostedfiltering of claim 1, further comprising: (a) controlling a resonantfrequency of each Q-boosted resonator; (b) wherein a substantially flatpass band is formed between the resonance frequencies of the twoQ-boosted resonators.
 7. The method of Q-boosted filtering of claim 6,wherein each Q-boosted resonator comprises: (a) a resonant structure;and (b) an input electrode, the output electrode, a feedback inputelectrode, and a feedback output electrode, each of said electrodescapacitively coupled to the resonant structure.
 8. The method ofQ-boosted filtering of claim 7, wherein controlling the resonantfrequency for one of the Q-boosted resonators comprises applying a biasvoltage between the resonant structure of the Q-boosted resonator andthe input electrode, the output electrode, the feedback input electrode,and the feedback output electrode, each of said electrodes capacitivelycoupled to the resonant structure.
 9. The Q-boosted resonator of claim2, wherein each resonant structure is selected from a group ofresonators consisting of: comb-driven resonators, piezo coupledresonators, ring resonators, contour mode ring resonators, wine-glassring resonators, Lame mode resonators, bar resonators, flexural beamresonators, membrane resonators, comb-driven flexural-mode resonators,center-supported disk resonators, surface acoustic wave (SAW) devices,bulk acoustic wave (BAW) devices, film bulk acoustic resonator (FBAR)devices, lateral overmoded bulk acoustic-wave resonator (LOBAR) devices,piezo actuated resonators, internal dielectric actuated resonators,internally-transduced resonators having a capacitive couple formed froma semiconductor junction, and combinations of the foregoing.
 10. TheQ-boosted resonator of claim 2, wherein each resonant structure issupported above a substrate by one or more anchors.
 11. The Q-boostedresonator of claim 10, wherein each resonant structure tuning voltage istransmitted through one or more of the anchors.
 12. A Q-boostedresonator, comprising: (a) a micromechanical resonant structure; (b) atleast four electrodes coupled to the resonant structure; (c) wherein theresonant structure is configured to be biased by a tuning voltagerelative to the electrode that is an input, the electrode that is anoutput, the electrode that is a feedback input, and the electrode thatis a feedback output; and (d) wherein the resonant structure has aresonant frequency that is changed by varying the tuning voltage; and(e) an amplifier, disposed between the feedback input electrode and thefeedback output electrode, that is configured to form a positivefeedback loop with the resonant structure; (f) wherein the positivefeedback loop is configured to increase or decrease an intrinsic Q ofthe resonant structure.
 13. The Q-boosted resonator of claim 12, whereineach amplifier comprises a negative-resistance amplifier.
 14. TheQ-boosted resonator of claim 12, wherein each resonant structure isselected from a group of resonators consisting of: comb-drivenresonators, piezo coupled resonators, ring resonators, contour mode ringresonators, wine-glass ring resonators, Lame mode resonators, barresonators, flexural beam resonators, membrane resonators, comb-drivenflexural-mode resonators, center-supported disk resonators, surfaceacoustic wave (SAW) devices, bulk acoustic wave (BAW) devices, film bulkacoustic resonator (FBAR) devices, lateral overmoded bulk acoustic-waveresonator (LOBAR) devices, piezo actuated resonators, internaldielectric actuated resonators, internally-transduced resonators havinga capacitive couple formed from a semiconductor junction, andcombinations of the foregoing.
 15. The Q-boosted resonator of claim 12,wherein each resonant structure is supported above a substrate by one ormore anchors.
 16. A Q-controlled resonator, comprising: (a) amicroelectromechanical system (MEMS) resonant structure; (b) at leastfour electrodes coupled to the MEMS resonant structure; (c) wherein theMEMS resonant structure is configured to be biased by a voltage VPrelative to a ground; (d) wherein the four electrodes comprise: (1) aninput electrode biased at V_(E1) relative to the ground; (2) an outputelectrode biased at V_(E2) relative to the ground; (3) a feedback inputelectrode; and (4) a feedback output electrode; (e) wherein the MEMSresonant structure has a resonant frequency that is changed by varyingthe tuning voltage V_(P); and (f) an amplifier, disposed between thefeedback input electrode and the feedback output electrode, configuredto form a feedback loop with the MEMS resonant structure; (g) whereinthe feedback loop is configured to either increase or decrease anintrinsic Q of the MEMS resonant structure.
 17. A Q-controlledresonator, comprising: (a) a microelectromechanical system (MEMS)resonant structure; (b) at least four electrodes coupled to the MEMSresonant structure; (c) wherein the four electrodes comprise: (1) aninput electrode biased at V_(E1) relative to the ground; (2) an outputelectrode biased at V_(E2) relative to the ground; (3) a feedback inputelectrode; and (4) a feedback output electrode; (d) wherein the MEMSresonant structure has a resonant frequency that is changed by varyingany of the voltages V_(E1) and V_(E2); and (e) an amplifier, disposedbetween the feedback input electrode and the feedback output electrode,configured to form a feedback loop with the MEMS resonant structure; (f)wherein the feedback loop is configured to either increase or decreasean intrinsic Q of the MEMS resonant structure.